Proof sin(10) is irrational.

  • #1

Homework Statement


Prove [itex] \sin{10} [/itex], in degrees, is irrational.


Homework Equations


None, got the problem as is.


The Attempt at a Solution


Im kinda lost.
 

Answers and Replies

  • #2
STEMucator
Homework Helper
2,075
140

Homework Statement


Prove [itex] \sin{10} [/itex], in degrees, is irrational.


Homework Equations


None, got the problem as is.


The Attempt at a Solution


Im kinda lost.

Okay, are you familiar with proof by contradiction?

Start by contradicting the statement :

Suppose that sin(10) is irrational.
 
  • #3
Dick
Science Advisor
Homework Helper
26,263
619

Homework Statement


Prove [itex] \sin{10} [/itex], in degrees, is irrational.


Homework Equations


None, got the problem as is.


The Attempt at a Solution


Im kinda lost.

Let x=sin(10). You'll want to find a polynomial x satisfies and show it has no rational root. Hint: sin(30)=1/2=sin(10+10+10).
 
  • #4
I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?
 
  • #5
13,169
7,067
yes and that means that sin(10) can be represented by the ratio of two integers a and b sin(10) = a/b

next step...
 
  • #6
Dick
Science Advisor
Homework Helper
26,263
619
I should suppose sin(10) is rational, if i am to contradict the statement, shouldnt i?

Zondrina's hint contains nothing of any real substance to start solving the problem. Mine does. I suggest you start trying it.
 

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